As shown in FIG. 1, a diagram illustrates an exemplary polygon mirror 1 that is an object to be measured according to the current invention. The polygon mirror 1 is used in image devices such as a digital copier and a laser printer for an optical writing system. The polygon mirror 1 is rotated at a high speed around a rotational axis 1b as indicated by an arrow for reflecting light beams from an optical source in order to scan the reflected beams that are reflected on a polygon mirror surface 1a. The polygon mirror surface 1a requires a highly precise configuration. A deviation from the predetermined design leads to an unexpected result in image point diameter and image position. Although the polygon mirror rotational speed depends upon a writing speed of a particular image device, recent polygon mirrors need a high rotational speed rotation for a high speed writing operation. At a high rotational speed, a deformation of the polygon mirror surface is experienced due to heat and centrifugal force. Since the reflected beam from the above deformed mirror surface fails to form an image on a predetermined position, there is a need for accurately measuring and evaluating the polygon mirror surface configuration during the high-speed rotation.
For the stationary polygon mirror surface measurement, an interferometer is used. However, since the interference fringe is not observed for the rotating polygon mirror surface, the configuration of the rotating polygon mirror surface is not measured by the interferometer. For measuring the configuration of the rotating polygon mirror surface, one prior art measuring device is disclosed in Japanese Patent 3017998. The prior art measuring device scans a laser beam onto a rotating polygon mirror surface for measuring a time difference in the reflected beams in order to detect a difference in a tilt position among the mirror surfaces. Thus, the configuration of the rotating polygon mirror surface is measured. However, since the above described prior art measuring device requires a mechanical operational part for scanning the beams, an operational mechanical error becomes a measuring error. At the same time, the measuring technique requires some time. Although the mechanical operational error is corrected by mirror reflection, additional components associated with the correction are necessary and their installment error and the subsequent positional error both contribute as additional sources of error. Furthermore, since the spatial resolution within the mirror surface depends upon the scanning beam diameter, a high resolution level is not generally expected. By reducing the beam diameter for a higher spatial resolution level, the measuring time becomes substantially longer.
Another prior art in Japanese Patent 3150239 discloses a measuring device for performing a dynamic configuration measurement at a high spatial resolution in the order of nanometer with short measurement time. The above measuring device measures a minute periodic vibration change. To accomplish the measurement, the above measuring device provides a predetermined delay between a period of an input signal into an object to be measured and another period of a signal to generate a pulse of light at a light source and measures the surface change based upon the difference between the two periods. This measuring device, however, assumes that the surface change of the object to be measured has perfect periodic vibration. Since the above described polygon mirror is mechanically rotated, it is almost impossible due to factors such as rotational eccentricity for a mirror surface to return to the exact position in the order of nanometer. That is, perfect vibration motion is difficult to achieve. Since the above measuring device measures the difference in the periods, a non-periodic portion in the object to be measured becomes a measurement error and an accurate measurement according to the above device is difficult.
Furthermore, an exemplary method in Japanese Patent 3150239 measures the surface change as a set of stationary image data by synchronizing with the signal to be given to the object to be measured to emit light from the light source. However, again, this technique makes it difficult to obtain the stationary image data since the synchronization between the light emittance and the object change is not maintained due to a non-periodic component in the movement of the object to be measured.
One method determines a surface configuration after a single interference image is recorded. In general, the method includes spatial modulation methods to determine a configuration based upon the spatial distribution of the interference stripes. For example, Fourier transformation as disclosed in “Fourier Transfer and Optical Applied Measurement,” in Hikari Gizyutsu Kontakuto Vol. 36, No 2 (1998). By combining this spatial modulation method and the above described method of Japanese Patent 3150239 for synchronizing the signal to the object to be measured with the light emittance pulse signal, the dynamic configuration of an object is measured after a single interference image is recorded. Even if the movement of the object has a non-periodic component or the interference stripes are not completely stationary, as long as an image at an arbitrary timing is recorded for the interference stripes, the dynamic configuration is measured. Thus, it is possible to measure the dynamic configuration of an object such as a polygon mirror with a non-periodic movement.
Unfortunately, the above combined method has a shortcoming. When a configuration is measured by the Fourier transformation method, the peak frequency of the spatially modulated interference stripes is detected and used. For example, the peak frequency obtained by the Fourier transformation of the interference stripes takes either positive or negative numbers. The positive and negative signs of the configuration measurement values are reversed. When the signs are reversed, it becomes unclear whether the surface is convex or concave. The sign of the peak frequency is determined by a relative angle between the reflected light from the object to be measured and the reference light. For example, the peak frequency sign varies in the horizontal direction when the reference mirror is tilted to the right or the left with respect to the object mirror to be measured. By the same token, the peak frequency sign varies in the vertical direction when the reference mirror is tilted to the top or the bottom with respect to the object mirror to be measured. The above relative tilt is arbitrarily varied according to a frequency change for the interference stripe change and a setting tilt error in setting an object to be measured in a measuring device. There are some situations where the peak frequency sign cannot be determined only by the interference stripes. For the above reason, the stationary configuration of the object is previously measured by a separate measuring device and a current device. By comparing the previously measured configuration by another device and the current device, the peak frequency sign and the configuration measurement sign are confirmed and or adjusted. However, the measurement process takes longer, as described above, due to the previous stationary measurements.
Another method determines a surface configuration based upon a microscope detection technique as disclosed in “Simultaneous Amplitude-Contrast And Quantitative Phase-Contrast Microscopy By Numerical Construction of Fresnel Off-Axis Holograms,” Ouyou Kougaku (Applied Optics) Vol 34, 38 (1999). The above microscopy technique measures dynamic configuration of a resonating mirror and an angle of the mirror with respect to the resonating base. In yet another method, the above measured dynamic configuration of a resonating mirror and the above measured angle of the mirror with respect to the resonating base are subject to a pulse-interference and a phase shift or a Fourier transformation. Furthermore, in a study, the interference stripes are generated on the rotating polygon mirror surface, and by detecting a change in the contrast of the interference stripes in response to a varying mirror rotational speed, the rotational speed distribution is measured for the object to be measured.
It remains desirable to provide a correct sign for the peak frequency so as to measure a configuration at a high precision level without much preparation. It also remains desirable to provide a correct sign for the configuration measurement.